Question

Show that a cyclic parallelogram is a rectangle.

Answer 1

Let ABCD be a cyclic parallelogram.

∠ A = ∠ C (opposite angles of a parallelogram are equal)

∠A + ∠ C = 180° (opposite angles of a cyclic quadrilateral are supplementary)

∠ A + ∠A= 180°


2∠A= 180°

∠A = 180/2 = 90°

∠C = ∠ A = 90°

Similarly,∠B = ∠ D = 90°

Since all four angles are 90°, Hence, ABCD is a rectangle

i.e a cyclic parallelogram is a rectangle.


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Hope this will help you.

Answer 2

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